利润最大化范里安英文

ChapterNineteenProfit-MaximizationEconomicProfitAfirmusesinputsj=1…,mtomakeproductsi=1,…n.Outputlevelsarey1,…,yn.Inputlevelsarex1,…,xm.Productpricesarep1,…,pn.Inputpricesarew1,…,wm.TheCompetitiveFirmThecompetitivefirmtakesalloutputpricesp1,…,pnandallinputpricesw1,…,wmasgivenconstants.EconomicProfitTheeconomicprofitgeneratedbytheproductionplan(x1,…,xm,y1,…,yn)ispypywxwxnnmm1111.EconomicProfitOutputandinputlevelsaretypicallyflows.(流量）E.g.x1mightbethenumberoflaborunitsusedperhour.（每小时劳动投入量）Andy3mightbethenumberofcarsproducedperhour.（每小时产出量）Consequently,profitistypicallyaflowalso;e.g.thenumberofdollarsofprofitearnedperhour.EconomicProfitHowdowevalueafirm?如何为一个公司订价？Supposethefirm’sstreamofperiodiceconomicprofitsis0,1,2,…andristherateofinterest.Thenthepresent-valueofthefirm’seconomicprofitstreamisPVrr012211()EconomicProfitAcompetitivefirmseekstomaximizeitspresent-value.一个竞争性企业为最大化利润流现值。How?EconomicProfitSupposethefirmisinashort-runcircumstanceinwhich（假定公司处于短期的生产环境）Itsshort-runproductionfunctionisyfxx(,~).12xx22~.EconomicProfitSupposethefirmisinashort-runcircumstanceinwhichItsshort-runproductionfunctionisThefirm’sfixedcostisanditsprofitfunctionisyfxx(,~).12pywxwx1122~.xx22~.FCwx22~Short-RunIso-ProfitLines短期等利润线A$iso-profitline（等利润线）containsalltheproductionplansthatprovideaprofitlevel$.A$iso-profitline’sequationispywxwx1122~.Short-RunIso-ProfitLinesA$iso-profitlinecontainsalltheproductionplansthatyieldaprofitlevelof$.Theequationofa$iso-profitlineisI.e.pywxwx1122~.ywpxwxp1122~.Short-RunIso-ProfitLines短期等利润线ywpxwxp1122~hasaslopeofwp1andaverticalinterceptofwxp22~.Short-RunIso-ProfitLinesyx1Slopeswp1Short-RunProfit-Maximization短期公司利润最大化Thefirm’sproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirm’sconstraintonchoicesofproductionplans.（给定公司的生产计划约束，使生产计划尽可能地达到最高的等利润线上。）Q:Whatisthisconstraint?（生产计划约束？）Short-RunProfit-MaximizationThefirm’sproblemistolocatetheproductionplanthatattainsthehighestpossibleiso-profitline,giventhefirm’sconstraintonchoicesofproductionplans.（生产计划的选择约束）Q:Whatisthisconstraint?（技术约束）A:Theproductionfunction.（生产函数）Short-RunProfit-Maximizationx1TechnicallyinefficientplansyTheshort-runproductionfunctionandtechnologysetforxx22~.yfxx(,~)12Short-RunProfit-Maximizationx1Slopeswp1yyfxx(,~)12Short-RunProfit-Maximizationx1ySlopeswp1x1*y*Short-RunProfit-Maximizationx1ySlopeswp1Givenp,w1andtheshort-runprofit-maximizingplanisx1*y*xx22~,(,~,).**xxy12Short-RunProfit-Maximizationx1ySlopeswp1Givenp,w1andtheshort-runprofit-maximizingplanisAndthemaximumpossibleprofitisxx22~,(,~,).**xxy12.x1*y*Short-RunProfit-Maximizationx1ySlopeswp1Attheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximaliso-profitlineareequal.x1*y*Short-RunProfit-Maximizationx1ySlopeswp1Attheshort-runprofit-maximizingplan,theslopesoftheshort-runproductionfunctionandthemaximaliso-profitlineareequal.MPwpatxxy1112(,~,)**x1*y*Short-RunProfit-MaximizationMPwppMPw1111pMP1isthemarginalrevenueproductofinput1,therateatwhichrevenueincreaseswiththeamountusedofinput1（要素1的边际产品收益）.Ifthenprofitincreaseswithx1.Ifthenprofitdecreaseswithx1.pMPw11pMPw11Short-RunProfit-Maximization;ACobb-DouglasExampleSupposetheshort-runproductionfunctionisyxx11/321/3~.Themarginalproductofthevariableinput1isMPyxxx1112321/313/~.Theprofit-maximizingconditionisMRPpMPpxxw1112321/313()~.*/Short-RunProfit-Maximization;ACobb-DouglasExamplepxxw312321/31()~*/Solvingforx1gives()~.*/xwpx123121/33Short-RunProfit-Maximization;ACobb-DouglasExamplepxxw312321/31()~*/Solvingforx1gives()~.*/xwpx123121/33Thatis,()~*/xpxw12321/313Short-RunProfit-Maximization;ACobb-DouglasExamplepxxw312321/31()~*/Solvingforx1gives()~.*/xwpx123121/33Thatis,()~*/xpxw12321/313soxpxwpwx121/313213221/233*//~~.Short-RunProfit-Maximization;ACobb-DouglasExamplexpwx113221/23*/~isthefirm’sshort-rundemandforinput1whenthelevelofinput2isfixedatunits.~x2Short-RunProfit-Maximization;ACobb-DouglasExamplexpwx113221/23*/~isthefirm’sshort-rundemandforinput1whenthelevelofinput2isfixedatunits.~x2Thefirm’sshort-runoutputlevelisthusyxxpwx**()~~.11/321/311/221/23ComparativeStaticsofShort-RunProfit-Maximization比较静态分析Whathappenstotheshort-runprofit-maximizingproductionplanastheoutputpricepchanges?ComparativeStaticsofShort-RunProfit-Maximizationywpxwxp1122~Theequationofashort-runiso-profitlineissoanincreaseinpcauses--areductionintheslope,and--areductionintheverticalintercept.ComparativeStaticsofShort-RunProfit-Maximizationx1Slopeswp1yyfxx(,~)12x1*y*ComparativeStaticsofShort-RunProfit-Maximizationx1Slopeswp1yyfxx(,~)12x1*y*ComparativeStaticsofShort-RunProfit-Maximizationx1Slopeswp1yyfxx(,~)12x1*y*ComparativeStaticsofShort-RunProfit-MaximizationAnincreaseinp,thepriceofthefirm’soutput,causes–anincreaseinthefirm’s